Question: Simplify; express your answer in exponential form. Assume $r\neq 0, z\neq 0$. $\dfrac{{(r^{-4})^{-4}}}{{(r^{5}z)^{2}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${r^{-4}}$ to the exponent ${-4}$ . Now ${-4 \times -4 = 16}$ , so ${(r^{-4})^{-4} = r^{16}}$ In the denominator, we can use the distributive property of exponents. ${(r^{5}z)^{2} = (r^{5})^{2}(z)^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(r^{-4})^{-4}}}{{(r^{5}z)^{2}}} = \dfrac{{r^{16}}}{{r^{10}z^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{16}}}{{r^{10}z^{2}}} = \dfrac{{r^{16}}}{{r^{10}}} \cdot \dfrac{{1}}{{z^{2}}} = r^{{16} - {10}} \cdot z^{- {2}} = r^{6}z^{-2}$.